For which function is f(x) equal to f-1(x)? a. f(x)=x+6/x-6 b. f(x)=x+2/x-2 c. f(x)=x+1/x-1 d. f(x)=x+5/x-5

Part C

Step-by-step explanation:

Part (i)

Let f(x)=y

let us solve the above equation for x and replace y with x in the final result

y(x-6)=x+6

xy-6y=x+6

xy-x=6y+6

taking x and 6 out side the bracket

x(y-1)=6(y+1)

replacing x with y

Hence Inverse not equal to the original function

hence Not true

Part (ii)

Let f(x)=y

let us solve the above equation for x and replace y with x in the final result

y(x-2)=x+2

xy-2y=x+2

xy-x=2y+2

taking x and 2 out side the bracket

x(y-1)=2(y+1)

replacing x with y

Hence Inverse not equal to the original function

hence Not true

Part (iii)

Let f(x)=y

let us solve the above equation for x and replace y with x in the final result

y(x-1)=x+1

xy-y=x+1

xy-x=y+1

taking x and 1 out side the bracket

x(y-1)=1(y+1)

replacing x with y

Hence Inverse equal to the original function

hence true

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.